The White House is considering economist Mohamed El-Erian as one of several candidates to serve as the Federal Reserve's vice chairman, according to a person familiar with the matter.

The process of selecting the central bank's No. 2 official began this month after President Donald Trump nominated Fed governor Jerome Powell to succeed Fed Chairwoman Janet Yellen when her term expires next February, and the search was described by people familiar with the process as still in its early stages.

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Mr. El-Erian, the former chief executive of Pacific Investment Management Co. and a former deputy director of the International Monetary Fund, is one of several candidates under consideration for the vice chair position, and no decisions have been made, according to the person familiar with the matter.

The White House has placed a heavy focus on selecting a vice chair with a strong background in monetary policy, this person said.

Separately, the White House is considering the nomination of a Kansas banking regulator for a seat on the Fed's board of governors, according to people familiar with the matter.

Michelle Bowman was confirmed as the Kansas bank commissioner in January and could be nominated to a spot reserved for a community banker or regulator of community banks. In 2014, Congress reserved one of seven seats on the Fed's board for a community banker and the position has never been filled.

Mr. Trump has an unusual opportunity to reshape the central bank's policy-making team during his first year in office. The Fed's powerful seven-member board of governors has three vacancies, including the seat for the vice chairman. He would have a fourth opening to fill if Ms. Yellen leaves the Fed after stepping down as chairwoman: Her term as governor expires in 2024.

Mr. Trump's first pick for the board, Randal Quarles, took office in October as Fed vice chairman of supervision.

Investors have been hungry for clues about how closely Mr. Trump's Fed nominees might hew to Ms. Yellen's policy of slowly raising interest rates from very low levels, especially given his criticism of her leadership during his campaign last year and his praise of her since taking office.

Mr. Trump has said he favors low interest rates and wants to see substantial deregulation.

Mr. Powell has voted reliably with Ms. Yellen during his five years on the Fed board, indicating no desire to chart a dramatic new policy course. But because he had little formal background in monetary policy before joining the central bank in 2012, the pick of the vice chairman has taken on greater significance.

Stanley Fischer resigned last month as the Fed's vice chairman, citing personal reasons, and the search for his replacement is now a priority for White House officials.

All Fed board nominations are subject to Senate confirmation.

A White House spokeswoman declined to comment, and Mr. El-Erian didn't immediately respond to a request for comment.

Mr. El-Erian resigned as Pimco's chief executive in 2014 and serves as chief economic adviser at Pimco's parent company, the German insurer Allianz. Mr. El-Erian, born in New York to an Egyptian father and a French mother, has master's and doctorate degrees in economics from Oxford University and has spoken and written frequently in recent years on monetary, regulatory and fiscal policy, including publishing a best-selling book on central banks last year titled "The Only Game In Town."

In recent years, Mr. El-Erian has voiced somewhat hawkish critiques of the Fed's policy stance, including decisions to hold interest rates at ultralow levels despite signaling plans to raise them. In recent months, he has suggested that the Fed's inflation target of 2% might be too high given structural forces holding down consumer prices.

He has signaled support for Mr. Trump's policies to reduce regulations and cut taxes, which he has said would allow the Fed to return monetary policy to more "normal" footing sooner than might otherwise occur. But Mr. El-Erian has warned against trade policies that hurt growth and send inflation too high.

Mr. El-Erian is on the board of the National Bureau of Economic Research, one of the country's most important research networks for academic economists, and was named by President Barack Obama to chair an advisory council on global development in 2012.

Ms. Bowman has been on the White House's radar since the summer and has gone through the internal vetting process for the job, said a person familiar with the process. The nomination hasn't been finalized and the White House could wait to announce the pick until it has concluded the search for the vice chair, said another person familiar with the process.

Ms. Bowman became vice president of her family's 135-year old Farmers & Drovers Bank in Council Grove, Kan., in 2010. From 2004 until 2009, she ran a government and public affairs consultancy in London.

Before that, she served in top positions at the then-newly created Department of Homeland Security and the Federal Emergency Management Agency in the George W. Bush administration, and she worked as a congressional adviser, including for former Sen. Bob Dole, the Kansas Republican.

Ms. Bowman didn't respond to a request for comment. Her candidacy was first reported by Politico.

Write to Nick Timiraos at nick.timiraos@wsj.com and Kate Davidson at kate.davidson@wsj.com